Two-dimensional high-resolution schemes and their application to the modeling of ionized waves of gas discharge

The method for constructing upwind high-resolution schemes is proposed in application to the modeling of ionizing waves in gas discharges. The flux-limiting criterion for continuity equations is derived using the proposed partial monotony property of a finite difference scheme. For two-dimensional extension, the cone transport upwind approach for constructing genuinely two-dimensional difference schemes is used. It is shown that when calculating rotations of symmetric profiles by using this scheme, a circular form of isolines is not distorted in a distinct from the coordinate splitting method. The conservative second order finite-difference scheme is proposed for solving the equations system of the drift-diffusion model of electric discharge; this scheme implies finite-difference conservation laws of electric charge and full electric current (fully conservative scheme). Computations demonstrate absence of numeric oscillations and good resolution of two-dimensional ionizing fronts in simulations of streamer and barrier discharges.